Amalgamated Engineering makes two kinds of gearbox – manual and automatic. There are four stages in the production of these, with details of times needed
and weekly availabilities given below. The company makes a profit of £64 on each manual gearbox sold and £100 on each automatic gearbox.
| Stage in
manufacture |
Time needed
(hours per unit) |
Time available
(hours per week) |
|
| Manual | Automatic | ||
| Foundry | 3 | 5 | 7,500 |
| Machine shop | 5 | 4 | 10,000 |
| Assembly | 2 | 1 | 3,500 |
| Testing | 1 | 1 | 2,000 |
(a) Find an optimal solution to the problem.
(b) The company can start making a new semiautomatic gearbox that needs 4, 4, 1 and 1 hour respectively in each manufacturing stage, and gives a profit of
£80 a unit. Should they make this new gearbox?
